JT Gravity Coupled to Fermions

TL;DR

This paper explores a solvable model of two-dimensional JT gravity coupled to fermions, revealing insights into quantum gravity near extremal black holes and proposing a UV completion with chaotic interactions.

Contribution

It introduces a new exactly solvable model of JT gravity coupled to fermions and proposes a UV completion that incorporates chaotic interactions and a novel gauge symmetry.

Findings

The model is exactly solvable in quantum field theory.

It violates certain principles expected in quantum gravity but can be cured with a cutoff and additional interactions.

The UV completion relates non-relativistic fermions to Weyl fermions via the AKK map.

Abstract

We argue that two-dimensional dilaton gravity models can all be derived from an analog of Jacobson's covariant version of the first law of thermodynamics. We then specialize to the JT gravity model and couple it to massless fermions. This model is exactly soluble in quantum field theory, and we present a new derivation of that result. The field theory model violates two principles one might want to impose on a quantum theory of gravity describing the near horizon region of an extremal charged black hole in four dimensions: finiteness of the entropy for finite causal diamonds, and the absence of global conservation laws. It preserves an infinite number of conservation laws that one would have expected to be violated, since the fermion state on each side of the $AdS_2$ wormhole is unavoidably thermal. We describe a cutoff version of the model, with extra interactions, which cures these difficulties. Our UV completion of the model depends on the AKK map of non-relativistic fermions in an inverted oscillator potential to Weyl fermions in Minkowski space. We argue that gauging the $Z_2$ symmetry of the oscillator model, using a density matrix with temperature that depends on the oscillator coordinates, and inserting chaotic interactions at (almost) infinite oscillator coordinate, we obtain a model with properties expected of quantum gravity in the near horizon region of an extremal charged black hole in four dimensions.